Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories

TL;DR

This work analyzes mass deformations of rank‑1 N=2 SCFTs by exploring Seiberg–Witten curves and their complex structure deformations under N=2 preserving conditions. It advances two complementary strategies: a direct, albeit challenging, discriminant‑factorization approach to identify sub‑maximal deformations, and a non‑systematic isogeny route (2‑ and 3‑isogenies) that yields explicit sub‑maximal deformations for several curves, including a notable $E_6$ deformation with $G_2$ flavor obtained via a 3‑isogeny. The authors compare new constructions to S‑duality predictions, refining central charges and Higgs‑branch data to constrain possible flavor symmetries and discriminant structures, and they develop central‑charge relations that tie Coulomb‑branch dimensions to Higgs and discriminant data. Overall, the paper expands the landscape of N=2 mass deformations for rank‑1 theories and demonstrates how duality inputs guide the identification and characterization of these deformations, with concrete results such as the $E_6$ submax deformation with $G_2$ flavor and partial progress toward other predicted submaximal cases.

Abstract

Turning on N=2 supersymmetry-preserving relevant operators in a 4-dimensional N=2 superconformal field theory (SCFT) corresponds to a complex deformation compatible with the rigid special Kahler geometry encoded in the low energy effective action. Field theoretic consistency arguments indicate that there should be many distinct such relevant deformations of each SCFT fixed point. Some new supersymmetry-preserving complex deformations are constructed of isolated rank 1 SCFTs. We also make predictions for the dimensions of certain Higgs branches for some rank 1 SCFTs.